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A276095 A nonlinear recurrence of order 4: a(1)=a(2)=a(3)=a(4)=1; a(n)=(a(n-1)+a(n-2)+a(n-3))^2/a(n-4).

%I A276095 #37 Aug 20 2024 14:55:11
%S A276095 1,1,1,1,9,121,17161,298978681,9933176210033041,
%T A276095 815437979830770470704295274609,
%U A276095 38747106750801481775941360512378545527545442200632960401
%N A276095 A nonlinear recurrence of order 4: a(1)=a(2)=a(3)=a(4)=1; a(n)=(a(n-1)+a(n-2)+a(n-3))^2/a(n-4).
%C A276095 All terms are perfect squares.
%H A276095 Seiichi Manyama, <a href="/A276095/b276095.txt">Table of n, a(n) for n = 1..15</a>
%F A276095 a(n) = A072878(n)^2.
%F A276095 a(n) = 16*a(n-1)*a(n-2)*a(n-3) - 2a(n-1) - 2a(n-2) - 2a(n-3) - a(n-4).
%F A276095 a(n)*a(n-1)*a(n-2)*a(n-3) = ((a(n) + a(n-1) + a(n-2) + a(n-3))/4)^2.
%t A276095 RecurrenceTable[{a[n] == (a[n - 1] + a[n - 2] + a[n - 3])^2/a[n - 4], a[1] == a[2] == a[3] == a[4] == 1}, a, {n, 1, 12}] (* _Michael De Vlieger_, Aug 18 2016 *)
%t A276095 nxt[{a_,b_,c_,d_}]:={b,c,d,(b+c+d)^2/a}; NestList[nxt,{1,1,1,1},10][[;;,1]] (* _Harvey P. Dale_, Aug 20 2024 *)
%o A276095 (Ruby)
%o A276095 def A(m, n)
%o A276095   a = Array.new(m, 1)
%o A276095   ary = [1]
%o A276095   while ary.size < n
%o A276095     i = a[1..-1].inject(:+)
%o A276095     j = i * i
%o A276095     break if j % a[0] > 0
%o A276095     a = *a[1..-1], j / a[0]
%o A276095     ary << a[0]
%o A276095   end
%o A276095   ary
%o A276095 end
%o A276095 def A276095(n)
%o A276095   A(4, n)
%o A276095 end
%Y A276095 Cf. A072878, A072882.
%K A276095 nonn
%O A276095 1,5
%A A276095 _Seiichi Manyama_, Aug 18 2016